It developed from an instrumental, "Groove Thang", that Martyn Ware and Ian Craig Marsh created earlier that year for Music for Stowaways, an album they released as British Electric Foundation.

"(We Don't Need This) Fascist Groove Thang" was written by Heaven 17 members Martyn Ware, Ian Craig Marsh and Glenn Gregory and included on their 1981 debut album Penthouse and Pavement.

German dark wave project Deine Lakaien featured a cover on the 1999 CD Maxi "Into My Arms" (as "(We Don't Need This) Fascist Groove Thing").

It was remixed by Inertia and The Crusher for the DEF CON 24 music compilation that same year, featuring multiple voice samples of American president elect Donald Trump.

American rock band LCD Soundsystem released a cover of the song on 2 November 2018, with the lyrics altered to reference Donald Trump instead of Reagan, and included it on their live album Electric Lady Sessions (2019).